Astronomy & Celestial Mechanics
the sky, computed
Concept

Dark matter halo — where it appears

The extended, roughly spherical mass distribution a galaxy sits inside, holding itself up by random motion rather than by rotation. It contains most of the system's mass and a few per cent of its coherent spin.

Named by 4 essays across one field — each of them below, with the objects they name alongside it.

A stream that is not the orbit it came from. 456 stars released in pairs from the two saddles of a 10⁵ solar-mass cluster over 4.0 billion years, integrated in a halo whose circular speed is 220 kilometres a second, drawn with the progenitor's own orbit. The cluster runs between 10 and 25 kiloparsecs and the orbit is the thin closed-looking curve; the stars are everything else. The point of the figure is the discrepancy. Stars leaving through the inner saddle are on slightly smaller orbits, turning round at a median of 24.77 kiloparsecs rather than the progenitor's 25.00, and therefore running ahead; stars leaving through the outer saddle reach 25.22 and fall behind. The whole spread is 1.8 per cent of the apocentre, which is the number worth carrying: an offset far too small to see in this drawing builds the entire stream, because it acts for four billion years. The two arms are therefore not merely displaced along the orbit, they are on different orbits, and the track a survey measures is a family of them rather than any single one. Fitting a Galactic potential by demanding that a stream lie along an orbit is wrong by exactly this much, and the size of the error grows with the mass of the progenitor, because the mass is what sets the distance between the two doors.

A stream is not the orbit it came from

A cluster torn apart by a galaxy leaves a thin trail of stars across the sky, and the obvious thing to do with it is fit an orbit. That is wrong by a knowable amount, because stars leave through two doors with a small energy offset and end up on a family of orbits rather than on one.

galaxies · Stellar streams A halo is born with a spin of a few hundredths. The distribution of the dimensionless spin parameter λ = J|E|^½ ÷ (G M⁵ᐟ²) across dark matter haloes, drawn as a lognormal of median 0.035 and logarithmic width 0.5, with the disc scale length each λ implies printed along the lower axis. The distribution is required to integrate to one and to peak at 0.0272, which is the median times e raised to minus sigma squared, and is the signature of a lognormal rather than of a bell curve drawn to look like one. λ is small because a halo is supported by random motion rather than by rotation: a value of 0.035 means the halo turns at about three and a half per cent of the rate it would need to hold itself up centrifugally. It is also nearly independent of halo mass, which is what points at a common origin. Mapping it to a disc through R_d = λ R₂₀₀/√2 with all of the specific angular momentum retained, a 10¹²-solar-mass halo of radius 206 kiloparsecs gives 5.1 kiloparsecs at the median, against the 2.6 kiloparsecs the Milky Way's disc actually has. The gap is not a failure of the estimate; it is the measurement that the baryons arrived with less spin per unit mass than the halo they arrived in.

A disc the size its halo was born with

A galaxy's mass says how much light it makes. It does not say how big it is. What sets a disc's size is a single dimensionless number describing how fast the dark halo around it happens to be turning — a number the disc had no part in choosing, distributed the same way for every halo mass in the universe.

galaxies · Galaxy spin Three mass models, one rotation curve. Rotation curves for three decompositions of the same galaxy, from a disc contributing 30 per cent of the outer rotation to one contributing 95. Each is the quadrature sum of a stellar disc, whose shape is fixed by the light distribution and whose amplitude is an unknown mass-to-light ratio, and a dark halo with parameters of its own. All three reproduce the same flat outer rotation, because the halo's amplitude is adjusted to make up whatever the disc does not supply. They differ in the inner few kiloparsecs, by 27 kilometres a second here — which is more than the measurement error and less than the uncertainty in the disc's own contribution, since that depends on a mass-to-light ratio nobody measures directly. The maximum-disc assumption picks the largest disc consistent with the data, and it is a convention rather than a result.

Three mass models that fit the same curve

A rotation curve is one function of radius and it is fitted with three components, only one of which is known. The stellar disc's contribution scales with a mass-to-light ratio nobody measures, and whatever the disc does not supply the dark halo does — so a family of models reproduces the same curve exactly, and choosing among them is a convention rather than a measurement.

galaxies · Dark matter Galaxy formation is inefficient nearly everywhere. Star formation efficiency — the stellar mass a halo has made, divided by the 0.157 of its mass that is baryons — against halo mass, by abundance matching. The n-th most numerous halo is assigned the n-th most numerous galaxy and nothing else is assumed: the halo count is a Sheth–Tormen mass function integrated from a linear power spectrum, the galaxy count is a measured double Schechter, and the matching is a monotone map between two cumulative counts. The curve peaks at 22 per cent, at a halo mass of 10^11.89 M☉, and falls to 0.6 per cent at the bottom of the range and 0.3 per cent at the top. A halo of the Milky Way's mass, 1.3·10¹² M☉, sits near the peak at 21 per cent — and near the peak means near the best any halo has ever managed. The two sides are two different problems and the figure cannot tell them apart: below the peak the shallow potential lets supernovae drive gas out, above it the gas falling in is shock-heated and cannot cool fast enough. What the abundance-matching assumption cannot show is scatter — it assigns one galaxy mass per halo mass by construction, and the real relation has about 0.15 dex of spread that this method is blind to by definition.

Two counts that are not the same shape

Dark matter halos are counted by a calculation that knows nothing about stars. Galaxies are counted by a survey. Laid on the same axes the two curves disagree at both ends and agree nowhere, and the knee is where the two disagreements hand over.

galaxies · Luminosity function

Named alongside it

The objects these essays reach for when they reach for this one.

Abundance matchingAdiabatic contractionAngular momentumBaryon fractionThe baryonic Tully–Fisher relationCooling timeDark matterDegeneracyThe disc–halo degeneracyDisc scale lengthDynamical frictionExponential disc

All concepts